I have cut open many a dead battery to find that neither the zinc can nor the carbon rod have been corroded. What exactly makes the battery die if the electrodes are still intact after death?
batteries need electrodes (which can be used up) and electrolyte (which can be used up), the electrolyte has to be in contact with unused electrode material and in a continuous path to the other electrode. lots of areas and reactions to cause a failure. these chemicals become contaminated, used up or not where they need to be to produce electricity.